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If $p$ is an odd prime expressible as
$$p=x^2+5y^2$$
where $x,y$ are integers, then prove that $p \equiv 1 \text{ or }9\text{ (mod 20)}$.
I made a mistake writing $\displaystyle p \equiv 4\ n^{2}\ \text{mod}\ 20$ instead of $\displaystyle p \equiv 4\ n^{2} + 5\ \text{mod}\ 20$, so that I corrected it... very sorry!How does (2) follows from (1)?
Balarka, the question is correct. You had interpreted it correctly.Ah, I see, I have interpreted the question wrong. I interpreted is as : p is an odd prime expressible as x^2 + 5y^2 if and only if p is 1 or 9 modulo 20.
But perhaps OP must have intended exactly this? Can Shobhit clarify whether he did a typo or not?
I see, thank you for clarifying.Shobhit said:Balarka, the question is correct. You had interpreted it correctly.